To treat a man with soft sawder is to flatter him, to “butter him up.”
But why? Well, sawder is an obsolete spelling of solder, and is still a phonetic spelling of a dialectal pronunciation of the word.
And solder, a low-melting alloy used for uniting certain metals, is derived from the Latin solidus, “solid.”
The transition from solidus to solder took place through a now obsolete verb form, sold (approximate pronunciation is sawd), meaning “to unite by soldering or welding.”
Now, one of the objects of flattery is to get the flatterer “in solid” with the person being flattered.
And soft solder is easier to apply than is the hard variety, even though it may be less durable.
The final link in this particular chain of evidence is obvious.